Why Mathematical Proof Is a Social Compact | Quanta Magazine

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Abstraction: Mathematical proof as community social compact, not pure objective truth

Key points:

Andrew Granville (Univ. Montreal) argues a proof's validity is established by community consensus, not abstract logic alone — verification means many experts examine it from different angles
Mochizuki's 500+ page claimed proof of the abc conjecture illustrates failure of the social compact: deliberately impenetrable, rejected community translation attempts
Axiom plurality: Hilbert showed any coherent, consistent starting set is worth exploring; ZFC is convention, not universal truth; Gödel proved some true statements are unprovable in any system
Paradigm shifts change what counts as valid: infinitesimals (Newton/Leibniz) were eventually replaced by epsilon-delta formalism
Proof assistants like Lean can verify proofs but are no more inherently reliable than human community review — only as good as the translation into their inputs
Granville is skeptical AI (e.g., ChatGPT) can generate fundamentally new proofs beyond its training data: "They are using word associations, not thinking"

Connections: Quanta Magazine · Mathematical Proof · Foundations Of Mathematics · Formal Verification